Question

Which equation could be used to solve for the measure of angle P?

Circle N is shown with a quadrilateral OPQR inscribed inside it. Angle O is labeled x degrees. Angle P is labeled y degrees. Angle Q is labeled z degrees. Angle R is labeled w degrees.

A. y+x=180
B. y + w = 180
C. y − (z + w) = 360
D. y + z + w = 360

Answer 1

y+w=180 is the answer.

Answer 2

Answer:

Correct choice is B

Step-by-step explanation:

Consider inscribed quadrilateral OPQR in the circle. In thes quadrilateral $m\angle O=x^{\circ},\ m\angle P=y^{\circ},\ m\angleQ=z^{\circ},\ m\angle R=w^{\circ}.$

By the Inscribed Quadrilateral Theorem, a quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary. Thus,

$m\angle O+m\angle Q=180^{\circ},\\ \\m\angle P+m\angle R=180^{\circ}$

or in terms of $x,\ y, z,\ w:$

$x^{\circ}+z^{\circ}=180^{\circ},\\ \\y^{\circ}+w^{\circ}=180^{\circ}.$

Hence, option B is true.